Prove that `(a^2sin(B-C))/(sinb+sinC)+(b^2"sin"(C-A))/(sinC+sinA)+(c^2"sin"(A-B))/(sinA+sinB)=0`

Explanation

`(a^2sin(B-C))/(sinB+sinC) = ((2RsinA)^2 sin(B-C))/(sinB+sinC)`

`=(4R^2sin^2Asin(B-C))/(sinB+sinC)`

`=(4R^2sinA*sinAsin(B-C))/(sinB+sinC)`

`=(4R^2sinA*sin(pi-(B+C)sin(B-C))/(sinB+sinC)`

`=(4R^2sinA*sin(B+C)sin(B-C))/(sinB+sinC)`

`=(4R^2sinA*(sin^2B-sin^2C))/(sinB+sinC)`

`=(4R^2sinA*(sinB+sinC)(sinB-sinC))/(sinB+sinC)`

`=4R^2sinA(sinB-sinC)`

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